Isospin multiplet

An isospin multiplet is an irreducible finite-dimensional SU(2) representation with labels $I,M$, where $I\ge 0$, $2I$ is an integer and $M=I,I-1,\dots ,-I$. With Hermitian generators, the lowering coefficient is $\sqrt{(I+M)(I-M+1)}$. The quadratic Casimir operator has value $I(I+1)$, fixing all ladder norms and the termination at $M=-I$.